Solve the following problems (1 - 6)

1.23. The trade union of the Faculty Office, which consists of 9 members, at its meeting shall elect a chairman, deputy chairman and treasurer. How many different occasions when this can be?

2.23. An urn 3 white and 7 black balls. What is the probability that a randomly extracted two balls will be black?

3.23. Three machines operate independently from each other. The probability that the first machine for the change fails, equal to 0.1, the second - and third 0.2 - 0.3. Find the probability that, during the change will fail: a) at least two machines; b) two machines; c) three machines.

4.23. The computer lab of 40% and 60% of calculators displays. When calculating the 90% and 80% of calculators displays running smoothly, a) Find the probability that a randomly taken computer will run smoothly at the time of calculation, b) the selected machine worked flawlessly during the calculation. What is the type most likely it belongs to?

5.23. The probability of hitting the target with one shot is equal to 0.8. Made 7 shots. Find the probability that there had been: a) Four defeats the purpose; b) six defeats; c) no more than six lesions.

6.23. The probability of occurrence of an event in each of the independent trials is 0.8. Find the probability that the event occurs 100 test not less than 70 and not more than 80 times.

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